Investigations on Yb-doped CW Fiber Lasers

Investigations on Yb-doped CW Fiber Lasers B.N. Upadhyaya *1, S. Kher 1, M.R. Shenoy 2, K. Thyagarajan 2, T.P.S. Nathan 1 1 Solid State Laser Division, Centre for Advanced Technology, Indore, India-452013 2 Department of Physics, IIT Delhi, India-110016 ABSTRACT Cladding pumped fiber lasers have been analyzed, based on numerical solution of steady state rate equations. It includes estimation of threshold, pump and signal evolution together with population inversion and gain along fiber length. Simulation results for a typical Yb-doped double clad fiber have been compared with the experiment. Development details of a Yb-doped fiber laser have also been provided. Keywords: Fiber Laser, Yb-doped double clad fiber, threshold pump power, gain, pump and signal evolution 1. INTRODUCTION Yb-doped double clad fiber lasers have attracted much attention due to their high efficiency, high power capability, compactness and reliability as compared to conventional solid-state lasers. The high power capability with diffraction limited beam quality makes it a natural choice for a wide range of material processing applications. High power pump diodes and the high damage threshold of the silica host allow Yb-doped fiber lasers to be scaled up to kw power level 1. The most widely used resonator configuration for fiber lasers is a Fabry-Perot cavity, in which at one end an ~100% reflectivity at lasing wavelength is achieved by means of a fiber Bragg gratings written in the fiber core and a 4% Fresnel reflection at the other cleaved end. Wide absorption band of Yb-doped fibers from ~800 to ~1064nm and lasing wavelengths from ~974 to ~980nm and ~1010 to ~1170nm makes it a unique laser source for various applications. It has two absorption peaks, one at 915nm and another at 975nm. The maximum absorption cross section occurs at 975nm and is widely used as the effective pump wavelength. It acts as a three-level system for emission at 975nm and as a high gain four-level system for emission in the range 1010-1170nm. 2 Although coupling of single clad single mode fibers from laser diodes is very poor, double clad rare earth doped fibers with clad pumping have been effectively used for development of efficient diode pumped fiber lasers. Absorption characteristics of double clad fibers are dependent on doping concentration as well as on the asymmetry introduced in the inner clad to avoid excitation of skew modes 3. Optimization of fiber laser performance necessitates investigation of cladding pumped fibers for its optimum parameters like cladding geometry, absorption, fiber length and pump geometry 4,5,6. Any such investigation of CW fiber lasers requires solution of steady state rate equations. As the rate equations involve absorption and emission cross-sections at pump and signal wavelength, McCumber relation 7 can be used to find the cross-section values. Analytical solutions for pump power threshold, optimum fiber length and gain have been provided by some authors based on assumption of absorption cross section at laser wavelength being very small in comparison with emission cross section at signal wavelength along with upper state population inversion being very small in comparison with doping concentration 4,8. In case of Yb-doped double clad fibers, if we take three level laser operation, the absorption cross section at 975nm is comparable to emission cross section at 975nm, so the analytical solutions are not good enough to describe laser operation at 975nm. Thus, an exact solution of steady state equations is necessary to analyze the Yb-doped fiber laser properties for all wavelengths of emission. In this paper, we have simulated a typical Yb-doped double clad fiber laser for quasi four-level operation and the same fiber has been used for experimental verification of simulation results. The simulation results provide the basis for analysis and optimization of experimental results. 2. THEORY For CW double clad fiber lasers with Fabry-Perot cavity as in Fig.1, the steady state rate equations are given by 3 1

[ Pp + ( z) + Pp ( z)] σapγp Γs + σa( λ )[ Ps + ( z, λ ) + Ps ( z, λ )] λdλ N 2( z) hνpa hca = N [ Pp + ( z) + Pp ( z)]( σap + σep) Γp 1 Γs + + [ σe( + σa( λ )][ Ps + ( z, + Ps ( z, ] λdλ hνpa τ hca (1) dpp ± ( z) ± = Γp[ σ apn + { σ 24 ( σap+ σep)} N 2( z)] P p ± ( z) α ( z, λ p) Pp ± ( z) dz (2) dps ± ( z, λ ) ± = Γs[{ σe( + σa( λ )} N 2( z) σa( N] Ps ± ( z, + Γsσe( λ ) N 2( z) P 0( α ( z, λ ) Ps ± ( z, dz (3) Fig.1: A schematic of fiber laser geometry where, N=N 1 (z)+n 2 (z) represents the doping concentration with N 1 and N 2 as the lower and upper level populations, plus and minus superscripts represent the propagation along positive and negative directions. σ a and σ e are the absorption and emission cross-sections with subscripts p for pump and subscript s for signal and τ is the upper state life time. Γ p =A/A inner clad and Γ s represent the power filling factor for pump and signal respectively. α is the scattering loss and σ 24 is the exited state absorption cross section. P 0 (=2hc 2 /λ 3 represents the contribution of the spontaneous emission into the propagating laser mode. ν p and ν s are the pump and signal frequency and A the area of fiber core. P p and P s represent the pump and signal power respectively. In eq.1, dλ refers to the line-width of laser output around the center lasing wavelength λ. These equations are subject to boundary conditions P + s (0)=R 1 P - s (0) and P - s (L)=R 2 P + s (L) where R 1 and R 2 are the reflectivity of rear mirror and output coupler and L the fiber length. For strong pumping conditions, the contribution of spontaneous emission is negligible and from eq.3, we have a conservation condition as below: P + s (0)P - s (0) = P + s (L)P - s (L) = P + s (z)p - s (z) (4) This conservation condition shows that product of forward and backward propagating signal is constant along the fiber length and can be used for finding the initial signal power, which satisfies the boundary conditions. As the equations are coupled, it can be solved numerically using fourth order Runga-Kutta method to find the laser characteristics. The saturation power for pump and signal are given by hνsa hνpa P s, sat =, P p, sat = (5) Γs( σes + σas) τ Γp( σep + σap) τ The output power is given by P out =(1-R 2 )P s +(L) (6) For strong pumping condition and quasi four-level operation of Yb-doped fiber laser, we have σ ep <<σ es and N 2 (z)<<n. Under these conditions, we have the analytical solutions for pump threshold (P p (0) th ), gain coefficient (g 0 (z)) and optimum fiber length (L opt ) given by 4,8 νp [ NΓsσa( λ s) L ln( R1R2 )]( ) Psat( NΓpσap+ αp) s P p (0) th = ν (7) NΓpσap[1 exp{ ( NΓpσap + αp) L}] g s (z)= 1+ [ Ps g 0( z) ( z) P + + s ( z)] / P NΓ pσappp( z) where, g 0 (z)= NΓ sσa( λs) νp ( ) Psat νs sat (8) (9) 2

F αs + NΓsσ a( λs) 1 L opt = α s g 0(0) + NΓsσa( λs) ln F F + R s α where, F= NΓ pσ ap+ αp, R (1 + R 2) R1 dps + ( z) = and = 0 for z=lopt R1 (1 R 2) + R 2 (1 R1) dz (10) 3. EXPERIMENT A Yb-doped laser fiber having an octagonal inner clad geometry with core diameter of 5µm and inner clad diameter of 125µm from Nufern, USA has been used for experimental set up of fiber laser. This fiber has a second mode cut-off at 960nm and ensures single mode diffraction limited output at the lasing wavelength. The fiber has an absorption of 1.7dB/m at 975nm. A 2Watt fiber coupled diode laser with center wavelength at 975nm at 25 C of operating temperature from Unique MODE GmbH, Germany has been used for pumping the 8m length of Yb-doped double clad fiber. The diode laser output has been collimated using a 50mm focal length lens and it has been further focused using another 50mm focal length lens to image the fiber tip on the laser fiber input end. A dichroic mirror, which transmits the pump wavelength and is highly reflecting in the laser output wavelength range of 1064-1140nm acts as the rear mirror, whereas the 4% Fresnel reflection at the output cleaved end acts as the output coupler for the fiber laser. Experiments were carried out using two schemes, in one of the schemes, the rear mirror has been butt-coupled with the fiber input end, whereas in the other scheme the rear mirror has been kept in between the collimating and focusing lenses. In case of butt-coupled mirror, as the mirror touches the fiber end, if the fiber end is not cleaved perfectly or any end face chipping leads to higher losses and a corresponding decrease in output power is achieved. The other scheme is free from such problems, since the mirror is kept between the lenses and the back reflected laser beam is focused back at the fiber end. However, in this scheme the lenses should have a broad band anti reflection coating from 975nm to 1140nm to avoid losses in the cavity. Fig.2(a) and 2(b) show the experimental arrangement of the two schemes. The unabsorbed pump power has been filtered using another dichroic mirror, which has a high reflection at pump wavelength and high transmission at the lasing wavelength. A lasing threshold of 240mW has been achieved with center lasing wavelengths at 1087nm and at 1093nm. Fig.3 shows the variation of output power with input pump power, which has a slope efficiency of 35%. A maximum output power of 600mW has been achieved at the maximum pump power of 2Watts. The laser output spectrum has been recorded using a monochromator set up and a large area InGaAs photodiode. Fig.4 shows the laser output spectrum, which has a FWHM of ~2nm for each peak. The relative intensity in volts corresponds to the output power converted to corresponding photodiode signal across a resistive load. The laser output is emitted in a cone angle of 300mrad corresponding to core numerical aperture and is single mode with diffraction limited beam quality. Fig.2(a): Butt-coupled laser cavity Fig.2(b): Fiber laser cavity with mirror between the collimating and focusing lenses 3

600 500 Output power(mw) 400 300 200 Slope Efficiency=35% 100 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 Input power(mw) Fig.3: Variation of laser output power with input pump power 7 6 Relative intensity(volt) 5 4 3 2 1 0 1076 1080 1084 1088 1092 1096 1100 1104 1108 Wavelength(nm) Fig.4: Yb-doped fiber laser output spectrum 4

4. RESULTS AND DISCUSSION Theoretical simulations were carried out for the Yb-doped double clad fiber used in the experiment. The following parameters have been used in the simulation: λ p =975nm, λ s =1090nm, σ ap =26x10-21 cm 2, σ ep =26x10-21 cm 2, σ as =1.4x10-23 cm 2, σ es =2x10-21 cm 2, α p =3x10-5 cm -1, α s =5x10-5 cm -1 τ=1ms, L=8m, absorption at 975nm=1.7dB/m, N=9.42x10 19 atoms/cm 3, core diameter=5µm, core NA=0.15, inner clad diameter=125µm, R 1 =98%, R 2 =4%, Γ p =0.0016, Γ s =0.82, P p (0)=2Watt. For this fiber, the saturation powers for pump and signal are 480mW and 21.6mW respectively. Fig.5 shows the simulated relative upper level population density along the fiber length and from this figure it is clear that N 2 (z)<<n for strong pumping condition. 0.07 0.06 0.05 N 2 (z)/n 0.04 0.03 0.02 0.01 0.00 0 1 2 3 4 5 6 7 8 Position(metre) Fig.5: Variation of relative population density along fiber length The variation of gain coefficient along fiber length is given in fig.6, which shows that gain is not uniform along fiber length and if we integrate the gain coefficient with respect to fiber length, total gain along the fiber length can be achieved. The lasing threshold can also be estimated using the gain and loss equality at threshold. The evolution of pump power (P p ), forward and backward signal power (P s + & P s - ) together with the conservation of product P s + (z)p s - (z) along fiber length is given in fig.7. Using this graph, an optimum fiber length and the variation of output power with input pump power can be estimated. A theoretical estimate of threshold is 63mW and an estimate of maximum output power at maximum pump power of 2Watt and at lasing wavelength of 1090nm is 1.58Watts. The calculated value of optimum fiber length is 10.33meter. From eq.7, we see that threshold pump power is a function of doping concentration, core cross-section, dopant fiber length, pump and lasing wavelengths and mirror reflectivities. During the experiment, we found that diode output spectrum varies with operating current and output power. At lower current values, the diode has a center wavelength at 970nm and it shifts to 975nm at maximum output power and current. Thus, the observed threshold value is higher than the estimated value. In absence of any wavelength selection device such as Fiber Bragg Grating, the output lasing wavelength depends on fiber length, doping concentration, pump wavelength and host composition. In case of wavelength selection devices in the cavity, the output lasing wavelength is fixed. We have not used any wavelength selection device in the experimental set up, so we have a broad output spectrum and also a lower output power as compared with the estimated output power. Theoretical estimates show that the laser can be further 5

optimized to achieve higher output power and a narrow spectral width. The output wavelength can also be tuned by means of grating. 1.2 1.0 0.8 Gain Coefficient (m -1 ) 0.6 0.4 0.2 0.0 0 1 2 3 4 5 6 7 8 Position (metre) Fig.6: Variation of gain coefficient along fiber length 2.25 2.00 1.75 1.50 P s + P p Power (Watt) 1.25 1.00 0.75 0.50 0.25 P s - + - P s P s 0.00 0 1 2 3 4 5 6 7 8 Position (metre) Fig.7: Evolution of pump along with forward and backward signal along fiber length 6

5. CONCLUSION We conclude that we have carried out a theoretical analysis of cladding pumped CW fiber lasers for optimization of Yb-doped double clad fiber laser performance. Fiber laser characteristics were estimated for a typical Yb-doped double clad fiber using the exact solution of steady state rate equations. An output power of 600mW from Ybdoped double clad fiber laser with simultaneous lasing at two center wavelengths of 1087nm and 1093nm together with a diffraction limited beam quality has been achieved. A comparison of theoretical estimates with experimental results provides the inputs for optimization of fiber laser performance. 6. REFERENCES 1. 500W continuous wave fiber laser with excellent beam quality: J. Limpert et.al., Electron. Lett., Vol.39, 645(2003) 2. An ytterbium-doped monomode fiber laser:broadly tunable operation fro 1.010 to 1.162µm and three level operation at 974nm: D.C. Hanna et.al., Journal of Modern Optics, Vol.37, No.4, 517(1990) 3. The absorption characteristics of circular, offset, and rectangular double-clad fibers: Anping Liu et.al., Optics Comm, Vol.132, 511(1996) 4. Strongly pumped fiber lasers: Ido Kelson et.al., IEEE J. Q.E., Vol.34, No.9, 1572(1998) 5. High Power Double-Clad fiber Lasers: L. Zenteno, J. Lightwave Tech., Vol.11, No.9, 1435(1993) 6. Ytterbium doped silica fiber lasers: versatile sources for the 1-1.2 µm region: H.M. Pask et.al., IEEE J. Selected Topics in Quantum Electronics, Vo.1, No.1, 2(1995) 7. Einstein relations Connecting Broadband Emission and Absorption Spectra: D.E. McCumber, Phys. Rev., Vol.136, A954(1964) 8. An approximate analytic solution of strongly pumped Yb-doped double clad fiber lasers without neglecting the scattering loss: Limin Xiao et.al., Optics Comm., Vol.230, 401(2004) * bnand@cat.ernet.in; phone 91-0731-2442319; fax 91-0731-2442300 7